::
> input the 24 words+passphrase one time
No
> always need to unlock the device with my pin and then make the hidden wallets visible with my passphrase each time.
Yes
> With the second option, not being able to input the passphrase on the Trezor itself (Model One) there would always exist the risk of my passphrase being compromised, wouldn’t it?
Yes, this is one of the differentiators between the Trezor-1 and Trezor-T